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Express the Integrand as a Sum of Partial Fractions and Evaluate

Question 82

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- 3x211x+4x33x2+2xdx\int \frac { 3 x ^ { 2 } - 11 x + 4 } { x ^ { 3 } - 3 x ^ { 2 } + 2 x } d x


A) 2lnx3lnx2+4lnx1+C2 \ln | x | - 3 \ln | x - 2 | + 4 \ln | x - 1 | + C
B) 2lnx+4lnx23lnx1+C2 \ln | x | + 4 \ln | x - 2 | - 3 \ln | x - 1 | + C
C) lnxlnx2+lnx1+C\ln | x | - \ln | x - 2 | + \ln | x - 1 | + C
D) 3lnx2+4lnx1+C- 3 \ln | x - 2 | + 4 \ln | x - 1 | + C

Correct Answer:

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